# PCA and constructing an index

Given a set of correlated securities and their corresponding closing prices, I am looking for a way to construct an index of these securities.

When applying PCA to obtain the principal components, how can I use or understand the output to construct an index?

For instance in matlab:

[coeff,score,latent,tsquared,explained,mu] = pca(prices)

• Not sure I understood what you are trying to do. The eigenvector i from the PCA is in fact the weights of an index that would track the -ith principal component. – Alex C Apr 24 '17 at 0:21
• Hmm clear. But if you choose lets say the first two PC to explain the variation, how do you derive then the weight for the j-th asset? – JohnAndrews Apr 24 '17 at 0:24
• I don't know. I would form a linear combination of the first two PC, weighted by the square roots of the respective eigenvalues (so the volatilities are properly taken into account). – Alex C Apr 24 '17 at 0:40